There are essentially two ways to specifying a set.
The first is to enumerate its members -- give a list of them.
We represent such a set by
listing its elements separated by commas and enclosed in braces, as follows
{ 5, 6, 7 }
Clearly this method is feasible only if the set has a small number of members.
Examples:
The second method of defining a set is to specify a property which is common to all members, and to its members only. This property is called a defining property.
Our notation for this second is as follows: A name or identifier is introduced which stands for any member of the set being specified.
This is then followed by a statement of the defining property of the set. These two elements are separated by a vertical bar and enclosed in braces.
An example: { n | n is a natural number and 3 n and n < 6 }
In English: n is a natural number and n greater than or equal to 3, and less than 6.
It is possible to write the defining property in a shorter way:
{ n | n is a natural number and 3 n < 6 }
Examples:
Last modified: 27/July/98 (12:14)